Feature selection is a machine learning technique that has many interesting applications in the area of brain- computer interfaces (BCIs). Here we show how automatic relevance determination (ARD), which is a Bayesian feature selection technique, can be applied in a BCI system. We present an computationally efficient algorithm that uses ARD to com- pute sparse linear discriminants. The algorithm is tested with data recorded in a P300 BCI and with P300 data from the BCI competition 2004. The achieved classification ac- curacy is competitive with the accuracy achievable with a support vector machine (SVM). At the same time the compu- tational complexity of the presented algorithm is much lower than that of the SVM. Moreover, it is shown how visualiza- tion of the computed discriminant vectors allows to gain in- sights about the neurophysiological mechanisms underlying the P300 paradigm.